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Contents

• V Full version
• 0 Introduction
• 1 Differentiation
• 1.1 Differentiation
• 1.2 Small o and big O notations
• 1.3 Methods of differentiation
• 1.4 Taylor's theorem
• 1.5 L'Hopital's rule
• 2 Integration
• 2.1 Integration
• 2.2 Methods of integration
• 3 Partial differentiation
• 3.1 Partial differentiation
• 3.2 Chain rule
• 3.3 Implicit differentiation
• 3.4 Differentiation of an integral wrt parameter in the integrand
• 4 First-order differential equations
• 4.1 The exponential function
• 4.2 Homogeneous linear ordinary differential equations
• 4.3 Forced (inhomogeneous) equations
• 4.4 Non-constant coefficients
• 4.5 Non-linear equations
• 4.6 Solution curves (trajectories)
• 4.7 Fixed (equilibrium) points and stability
• 4.8 Discrete equations (Difference equations)
• 5 Second-order differential equations
• 5.1 Constant coefficients
• 5.2 Particular integrals
• 5.3 Linear equidimensional equations
• 5.4 Difference equations
• 5.5 Transients and damping
• 5.6 Impulses and point forces
• 5.7 Heaviside step function
• 6 Series solutions
• 7 Directional derivative
• 7.1 Gradient vector
• 7.2 Stationary points
• 7.3 Taylor series for multi-variable functions
• 7.4 Classification of stationary points
• 7.5 Contours of f(x, y)
• 8 Systems of differential equations
• 8.1 Linear equations
• 8.2 Nonlinear dynamical systems
• 9 Partial differential equations (PDEs)
• 9.1 First-order wave equation
• 9.2 Second-order wave equation
• 9.3 The diffusion equation